Problem: Simplify the following expression: $t = \dfrac{z^2 + 11z + 10}{z + 10} $
First factor the polynomial in the numerator. $ z^2 + 11z + 10 = (z + 10)(z + 1) $ So we can rewrite the expression as: $t = \dfrac{(z + 10)(z + 1)}{z + 10} $ We can divide the numerator and denominator by $(z + 10)$ on condition that $z \neq -10$ Therefore $t = z + 1; z \neq -10$